1. Field of the Invention
The present invention relates to underground media exploitation.
2. Description of the Prior Art
Local phenomena that may occur near a well, such as damage, have a tremendous impact on the injectivity or the productivity of a well. In the petroleum industry, it is very important to predict injectivity or productivity, especially when there are formation alterations in the vicinity of wells, which change the injection or production capacity of the well.
Great efforts have been made for a long time by use of experimental techniques, in the laboratory, or numerical modelling methods, in order to take into account these local phenomena near wells, as well as their impact on injectivity or productivity.
Numerical methods for modelling fluid flows within a well (injectivity and productivity of a well) comprise constructing two distinct models: the reservoir model and the near-wellbore model.
A reservoir model comprises two elements:
a grid, referred to as reservoir grid, having a set of cells that spatially discretize the reservoir and
a flow simulator. The flow simulator is a software for modelling fluid flows within a porous medium within the reservoir grid. This software simulates dynamic data/properties of the fluids (water, oil, gas): pressure, flux (amount of matter crossing a surface), saturation, flow rates or concentrations. For example, a simulator allows estimation, for a given well exploitation scenario (production scenario or injection scenario) and for a given time interval water, oil and gas saturations and oil, gas and water flow rates, water cut (water fraction in the liquid production), GOR (gas and oil ratio in the production), concentrations in polymer absorbed on the rock of the porous medium and the polymer injection flow rates, if a polymer solution is injected into the reservoir by an injection well, etc.
A near-wellbore model comprises two elements:
a grid, referred to as a “near-wellbore grid,” having a set of cells spatially discretizing the well and its surroundings. Its surroundings therefore belong to the porous medium in which the well is drilled; and
a flow simulator simulating with the near-wellbore grid, dynamic data/properties of the fluids (water, oil, gas).
The reservoir model and the near-wellbore model are generally autonomous and decoupled. Local phenomena are generally limited to the immediate vicinity of the well (to distances measured from centimeters to meters). Very small cells are necessary for the near-wellbore grid whereas larger cells are used for reservoir grids to accelerate calculations.
There are known techniques which use a single reservoir flow simulator for these two grids. It is for example possible to use the technique referred to as a “hybrid grid” combining, within a single grid, cells for the reservoir grid and cells for a locally refined grid of the near-wellbore region. A single flow simulator is associated with this grid type so as to better account for the behaviors of flows in the vicinity of the well in a field simulation.
However, simultaneous flow simulations in the reservoir, which require a very large number of cells, and in the areas close to the well with smaller cells, which require small time steps to provide calculation stability, pose numerical calculation problems, in particular the problem of calculating time (CPU time).
Domain decomposition techniques, described for example by GAIFFE, S. “Maillages Hybrides et Décomposition de Domaine pour la Modélisation des Réservoirs Pétroliers”, Ph.D. Thesis, Paris 6 University, 2000, and windowing techniques, described for example in the following document: MLACNIK, M. J. and HEINEMANN, Z. E. “Using Well Windows in Full Field Reservoir Simulation”, paper SPE 66371 presented at the SPE Reservoir Simulation Symposium, Houston, Tex., U.S.A., February 2001, have thus been developed.
Some delicate points such as convergence, stability or calculating time however pose problems in industrial applications. Furthermore, the domain decomposition method is not always “conservative” (deterioration of the mass balance in the model as a function of time), which is not suitable for practical use of the method. Besides, all these techniques require reformulation of the mathematical equations and of the boundary conditions developed in the flow simulators and new developments are necessary to integrate the near and far well solutions in a single model, which is a long and difficult task.